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MA20219: Analysis 2B

Follow this link for further information on academic years Academic Year: 2016/7
Further information on owning departmentsOwning Department/School: Department of Mathematical Sciences
Further information on credits Credits: 6      [equivalent to 12 CATS credits]
Further information on notional study hours Notional Study Hours: 120
Further information on unit levels Level: Intermediate (FHEQ level 5)
Further information on teaching periods Period:
Semester 2
Further information on unit assessment Assessment Summary: EX 100%
Further information on unit assessment Assessment Detail:
  • Examination (EX 100%)
Further information on supplementary assessment Supplementary Assessment:
MA20219 Mandatory extra work (where allowed by programme regulations)
Further information on requisites Requisites: Before taking this module you must take MA20218
Further information on descriptions Description: Aims:
To extend the theory of differentiation from functions of one real variable to functions of several real variables and to functions of one complex variable. To understand the relationship between these theories, their geometrical interpretation, and their application through examples.

Learning Outcomes:
After taking this unit students should be able to:
* state definitions and theorems in real and complex analysis and present proofs of the main theorems
* construct their own proofs of simple unseen results and of simple propositions
* present mathematical arguments in a precise, lucid and grammatical fashion
* apply definitions and theorems to simple examples
* give a geometric interpretation of multivariate differentiation
* evaluate simple contour integrals in the complex plane.

Skills:
Numeracy T/F A
Problem Solving T/F A
Spoken and Written Communication F (in tutorials and on problem sheets)

Content:
Frechet derivative as best linear approximation, partial and directional derivatives.
Continuous differentiability, Jacobian matrix, chain rule, higher order partial derivatives, equality of continuous 2nd derivatives. Exterior derivative of a 1-form (covector field), divergence and curl of a vector field, Hessian, stationary points and second derivative test, Taylor's theorem.
Complex differentiable functions and the Cauchy-Riemann equations, Curves in C, contour integrals. Primitives, Cauchy's theorem, Cauchy's Integral Formula, representation by power series. Liouville's Theorem, Fundamental Theorem of Algebra. Principal parts, Residue Theorem.
Further information on programme availabilityProgramme availability:

MA20219 is Compulsory on the following programmes:

Department of Computer Science
  • USCM-AFB20 : BSc(Hons) Computer Science and Mathematics (Year 2)
  • USCM-AAB20 : BSc(Hons) Computer Science and Mathematics with Study year abroad (Year 2)
  • USCM-AKB20 : BSc(Hons) Computer Science and Mathematics with Year long work placement (Year 2)
  • USCM-AFM14 : MComp(Hons) Computer Science and Mathematics (Year 2)
  • USCM-AAM14 : MComp(Hons) Computer Science and Mathematics with Study year abroad (Year 2)
  • USCM-AKM14 : MComp(Hons) Computer Science and Mathematics with Year long work placement (Year 2)
Department of Mathematical Sciences Department of Physics

MA20219 is Optional on the following programmes:

Department of Economics Department of Mathematical Sciences

Notes: